Internal problem ID [11575]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 244
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=3 x-y \left (t \right )+1\\ y^{\prime }\left (t \right )&=x+y \left (t \right )+2 \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 32
dsolve([diff(x(t),t) = 3*x(t)-y(t)+1, diff(y(t),t) = x(t)+y(t)+2, x(0) = 1, y(0) = 2],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {3}{4}+{\mathrm e}^{2 t} \left (-\frac {3 t}{2}+\frac {7}{4}\right ) \] \[ y \left (t \right ) = -\frac {5}{4}+{\mathrm e}^{2 t} \left (-\frac {3 t}{2}+\frac {13}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 42
DSolve[{x'[t]==3*x[t]-y[t]+1,y'[t]==x[t]+y[t]+2},{x[0]==1,y[0]==2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} \left (e^{2 t} (7-6 t)-3\right ) y(t)\to \frac {1}{4} \left (e^{2 t} (13-6 t)-5\right ) \end{align*}